Question: Solve for $x$ and $y$ using elimination. $\begin{align*}9x-3y &= 3 \\ 2x-2y &= -7\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $3$ $\begin{align*}-18x+6y &= -6\\ 6x-6y &= -21\end{align*}$ Add the top and bottom equations. $-12x = -27$ Divide both sides by $-12$ and reduce as necessary. $x = \dfrac{9}{4}$ Substitute $\dfrac{9}{4}$ for $x$ in the top equation. $9( \dfrac{9}{4})-3y = 3$ $\dfrac{81}{4}-3y = 3$ $-3y = -\dfrac{69}{4}$ $y = \dfrac{23}{4}$ The solution is $\enspace x = \dfrac{9}{4}, \enspace y = \dfrac{23}{4}$.